Non-parametric frequency identification and estimation in mean function for almost periodically correlated time series

The aim of this article is to present a non-parametric way to identify and estimate the unknown frequencies in the Fourier representation of mean function for almost periodically correlated time series. We state the exact form of asymptotic distribution of normalized estimator of Fourier coefficient for fixed frequency in considered class of time series. Next, we prove the consistency of subsampling procedure applied for the Fourier coefficient. Based on these results we propose a graphical method for determining the presence of periodic or almost periodic structure of mean function. Finally, following Walker (1971) [37] we construct a consistent estimator of frequency and corresponding Fourier coefficient.